Probing Chirality of the Quantum Hall Effect via the Landauer–Büttiker Formalism with Two Current Sources

Kyung Ho Kim ()
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Kyung Ho Kim: Department of Physics and Astronomy, Sejong University, Seoul 05006, Republic of Korea

Mathematics, 2025, vol. 13, issue 18, 1-10

Abstract: The quantum Hall effect is a paradigmatic example of topological order, characterized by precisely quantized Hall resistance and dissipationless edge transport. These edge states are chiral, propagating unidirectionally along the boundary, and their directionality is determined by the external magnetic field. While chirality is a central feature of the quantum Hall effect, directly probing it remains experimentally nontrivial. In this study, we introduce a simple and effective method to probe the chirality of edge transport using two independently controlled current sources in a Hall bar geometry. The system under investigation is monolayer epitaxial graphene grown on a silicon carbide substrate, exhibiting robust quantum Hall states. By varying the configurations of the two current sources, we measure terminal voltages and analyze the transport characteristics. Our results demonstrate that the observed behavior can be understood as a linear superposition of chiral contributions to the edge transport. This superposition enables tunable combinations of longitudinal and Hall resistances and enables additive or canceling behavior of Hall voltages depending on current source configuration. The Landauer–Büttiker formalism provides a quantitative framework to describe these observations, capturing the interplay between edge state chirality and the measurement configuration. This research offers a simple yet effective experimental and analytical approach for probing chiral edge currents and highlights the linear superposition principle in the quantum Hall effect.

Keywords: quantum Hall effect; edge states; topological protection; linear superposition; Landauer–Büttiker formalism; two current sources (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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